Tan(x) & Unit Circle - Degrees

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2014-01-07 03:50

In collections Trigonometry: Basic and More

This example demonstrates the relationship between angle α in degrees and the value of tan(α) using the unit circle through an animation. Core math concepts include the unit circle, trigonometric functions, angle measurement, and geometric construction. It is constructed using GeoGebra commands like Line, Circle, Intersect, Rotate, Angle, Segment, Distance, OrthogonalLine, Midpoint, Point, with objects such as α, RadianAlpha, up, O, B, a, c, C, D, cosine, sine, tangent, etc. Suitable for high school mathematics education to help students understand the definition of trigonometric functions and the application of the unit circle.

GeoGebra Commands & Parameters

Line(B, O) → a
Circle(O, 1) → c
Intersect(c, a, 2) → C
Rotate(C, α, O) → D
Angle(C, O, D) → β
Segment(O, D) → b
Distance(D, a) → d
OrthogonalLine(D, a) → e
Intersect(a, e) → A_2
Segment(D, A_2) → g
Segment(A_1, D_1) → h
Midpoint(D, A_2) → E1
Midpoint(A_1, D_1) → F
Point(xAxis) → G
Segment(G, A_1) → i
Intersect(c, a, 2) → A
Intersect(c, a, 1) → I
Segment(I, A) → j
Intersect(c, j, 2) → J
Segment(O, A_2) → l
Midpoint(O, D) → K
Midpoint(O, A_2) → E2

AI Drawing Prompt Reference

Draw a unit circle and label the angle α. Demonstrate the relationship between the angle α and its tangent value using an animation. Include the arc corresponding to angle α, the sine and cosine lines. Mark the point on the unit circle corresponding to angle α, draw the tangent line at that point, and show the length of the tangent line. Also, display the intersection of the tangent line with the x-axis and connect this point to the point on the unit circle to form a right triangle.

The prompt above was compiled from the original drawing commands and is for reference only.